(1 pt) Find the exact value (NO DECIMALS) of each expression by sketching a triangle:

A) sin(cos^-1(3/5))

b) cos(sin^-1(4/5))

I have no idea where to start

Printable View

- November 26th 2012, 08:18 AMRD33Trig expressions
(1 pt) Find the exact value (NO DECIMALS) of each expression by sketching a triangle:

A) sin(cos^-1(3/5))

b) cos(sin^-1(4/5))

I have no idea where to start - November 26th 2012, 08:39 AMfkfRe: Trig expressions
**A)**

Use the fact thatcos^2(x)+sin^2(x) = 1

We havecos^-1(3/5) <=> cos(x) = 3/5 => cos^2(x) = 9/25

Using the trigonometric one we get9/25+sin^2(x) = 25/25 <=> sin^2(x) = 16/25 <=> sin(x) = +/- 4/5But since cos^-1 is defined for 0 to pi, the only solution is sin(x) = 4/5

By this we now have the expressionsin(cos^-1(3/5)) = sin(sin^-1(4/5)) = 4/5

I leave the second one as exercise for you! (Nod) - November 26th 2012, 09:14 AMRD33Re: Trig expressions
Thank you. I got the second one right honestly by guessing.

Cos(sin^-1(4/5))

I got sin(x)=4/5

Sin^2= 16/25

And I'm not sure where to go from there - November 26th 2012, 12:25 PMfkfRe: Trig expressions